https://file.aiquickdraw.com/mathbot/file/1725899090087r0b2mjdw.jpg

The function given in the image is:

\[
y = \frac{x^5 + 4x^2}{x^2}
\]

First, let's simplify the function:

\[
y = \frac{x^5}{x^2} + \frac{4x^2}{x^2}
\]

This simplifies to:

\[
y = x^{5-2} + 4x^{2-2} = x^3 + 4
\]

Now, let's find the derivative of \(y\) with respect to \(x\):

\[
\frac{dy}{dx} = \frac{d}{dx}\left(x^3 + 4\right)
\]

The derivative of \(x^3\) is \(3x^2\) and the derivative of the constant 4 is 0.

So, the derivative is:

\[
\frac{dy}{dx} = 3x^2
\]

Would you like more details on any specific step or have any other questions?

Here are some related questions you might find useful:
1. How do you find the derivative of a product of two functions?
2. What is the power rule in differentiation?
3. How do you apply the chain rule to find derivatives?
4. How do you find the second derivative of a function?
5. What is the significance of the derivative in calculus?

**Tip:** When simplifying a rational function before differentiation, always look for opportunities to cancel out terms to make the differentiation easier.

Find the derivative of the function y = (x^5 + 4x^2) / x^2

Learn how to find the derivative of the function y = (x^5 + 4x^2) / x^2. This involves simplifying the rational expression and using the power rule for differentiation. Suitable for students in Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation